So your dictionary defines ‘sex’ as
that by which an animal or plant is male or female: the quality of being male or female
‘male’ as
Adj. masculine: of or pertaining to the sex that begets (not bears) young; or produces relatively small gametes.(Then there is a botanical version.)
‘female’ as
noun. a woman or girl. Any animal or plant of the same sex as a woman. Adj. of the sex that produces young or eggs, fructifications or seeds. of the sex characterised by relatively large gametes.
These 1990 definitions from your Chambers Dictionary could not be more biological. Begetting or bearing young, having relatively small or relatively large gametes, producing eggs or seeds.
The person who oversaw the 2010 Equalities Act only 10 years after your dictionary, was Harriet Hartman b. 1950 so aged sixty at the time. It seems likely she would have had a similar idea of what sex meant as that described in that dictionary.
As Janice Turner said:
Lady Haldane’s judgment on the Equality Act 2010 is extraordinary. She argues that if those who drafted the legislation had believed sex was only “biological” they would have included that word. Yet back then, before gender ideology infected public policy, no one dreamt that “sex” could mean anything but material reality.